Geodesic
Efficiency of cancer treatments: in silico experiments
Elena Piretto1, 2 ; Marcello Delitala1 ; Mario Ferraro3
1 Department of Mathematical Sciences, Politecnico di Torino, Italy.
2 Department of Mathematics, Universitá degli Studi di Torino, Italy.
3 Department of Physics, Universitá degli Studi di Torino, Italy.
Mathematical modelling of natural phenomena, Tome 15 (2020), article no. 19.

Voir la notice de l'article provenant de la source EDP Sciences

Despite the advances in the formulation of different therapies to fight cancer, the design of successful protocols is still a challenging problem. In order to provide some indications on the effectiveness of medical treatments, results from in silico experiments are presented based on a mathematical model comprising two cancer populations competing for resources and with different susceptibilities to the action of therapies. The focus is on the outcome of protocols in which the total dose can be administered with different time distributions. An efficiency index is proposed to quantify the effectiveness of different protocols. Simulations show that a standard dose chemotherapy is effective when the sensitive clone has a marked competitive advantage, whereas its outcome is much worse when a resistant clone emerges; obviously combinations of immune and chemotherapy work better. These results, in accord with previous finding reported in the literature, stress the importance to take into account competitive interactions among cancer clones to decide which therapeutic strategy should be adopted. However, it is not just the efficiency that changes in these different configurations of clonal composition and therapy timing. A general rule seems to emerge: when evolutionary pressures are strong, the best protocols entail and early starting of the treatment, whereas, on the contrary, when interactions among clones are weak, therapy should start later. Finally the model has been adapted to investigate the relative efficiency of different protocols, by using data reported in literature regarding experiments with breast cancer cells.
DOI : 10.1051/mmnp/2019031

Elena Piretto 1, 2 ; Marcello Delitala 1 ; Mario Ferraro 3

1 Department of Mathematical Sciences, Politecnico di Torino, Italy.
2 Department of Mathematics, Universitá degli Studi di Torino, Italy.
3 Department of Physics, Universitá degli Studi di Torino, Italy. 
@article{MMNP_2020_15_a38,
     author = {Elena Piretto and Marcello Delitala and Mario Ferraro},
     title = {Efficiency of cancer treatments: in silico experiments},
     journal = {Mathematical modelling of natural phenomena},
     eid = {19},
     publisher = {mathdoc},
     volume = {15},
     year = {2020},
     doi = {10.1051/mmnp/2019031},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/articles/10.1051/mmnp/2019031/}
}
TY  - JOUR
AU  - Elena Piretto
AU  - Marcello Delitala
AU  - Mario Ferraro
TI  - Efficiency of cancer treatments: in silico experiments
JO  - Mathematical modelling of natural phenomena
PY  - 2020
VL  - 15
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/articles/10.1051/mmnp/2019031/
DO  - 10.1051/mmnp/2019031
LA  - en
ID  - MMNP_2020_15_a38
ER  - 
%0 Journal Article
%A Elena Piretto
%A Marcello Delitala
%A Mario Ferraro
%T Efficiency of cancer treatments: in silico experiments
%J Mathematical modelling of natural phenomena
%D 2020
%V 15
%I mathdoc
%U https://geodesic-test.mathdoc.fr/articles/10.1051/mmnp/2019031/
%R 10.1051/mmnp/2019031
%G en
%F MMNP_2020_15_a38
Elena Piretto; Marcello Delitala; Mario Ferraro. Efficiency of cancer treatments: in silico experiments. Mathematical modelling of natural phenomena, Tome 15 (2020), article  no. 19. doi : 10.1051/mmnp/2019031. https://geodesic-test.mathdoc.fr/articles/10.1051/mmnp/2019031/

[1] N. André, M. Carré, E. Pasquier Metronomics: towards personalized chemotherapy? Nat. Rev. Clin. Oncol. 2014 413 431

[2] N. Bellomo, N. Li, P.K. Maini On the foundations of cancer modelling: selected topics, speculations, and perspectives Math. Models Methods Appl. Sci 2008 593 646

[3] A. Besse, G. Clapp, S. Bernard, F. Nicolini, D. Levy, T. Lepoutre Stability analysis of a model of interaction between the immune system and cancer cells in cml Bull. Math. Biol 2017 1084 1110

[4] S. Bunimovich-Mendrazitsky, H. Byrne, L. Stone Mathematical model of pulsed immunotherapy for superficial bladder cancer Bull. Math. Biol 2008 2055 2076

[5] C. Carrère Optimization of an in vitro chemotherapy to avoid resistant tumours J. Theor. Biol 2017 24 33

[6] L.G. De Pillis, A. Radunskaya A mathematical tumor model with immune resistance and drug therapy: an optimal control approach Comput. Math. Methods Med 2001 79 100

[7] L.G. De Pillis, W. Gu, A.E. Radunskaya Mixed immunotherapy and chemotherapy of tumors: modeling, applications and biological interpretations J. Theor. Biol 2006 841 862

[8] V.T. Devita, P. S. Schein The use of drugs in combination for the treatment of cancer: rationale and results New England J. Med 1973 998 1006

[9] A. D’Onofrio, U. Ledzewicz and H. Schättler, On the dynamics of tumor-immune system interactions and combined chemo-and immunotherapy, in New Challenges for Cancer Systems Biomedicine. Springer, Berlin (2012) 249–266.

[10] R. Eftimie, J.L. Bramson, D.J. Earn Interactions between the immune system and cancer: a brief review of non-spatial mathematical models Bull. Math. Biol 2011 2 32

[11] F. Frascoli, P.S. Kim, B.D. Hughes, K.A. Landman A dynamical model of tumour immunotherapy Math. Biosci 2014 50 62

[12] R.A. Gatenby, J. Brown, T. Vincent Lessons from applied ecology: cancer control using an evolutionary double bind Cancer Res 2009 7499 7502

[13] M. Gerlinger, C. Swanton How darwinian models inform therapeutic failure initiated by clonal heterogeneity in cancer medicine Br. J. Cancer 2010 1139 1143

[14] N. Hartung, C.T.-K. Huynh, C. Gaudy-Marqueste, A. Flavian, N. Malissen, M.-A. Richard-Lallemand, F. Hubert, J.-J. Grob Study of metastatic kinetics in metastatic melanoma treated with b-raf inhibitors: introducing mathematical modelling of kinetics into the therapeutic decision PloS One 2017 e0176080

[15] N.L. Komarova, J.A. Burger, D. Wodarz. Evolution of ibrutinib resistance in chronic lymphocytic leukemia (cll) Proc. Natl. Acad. Sci 2014 13906 13911

[16] V.A. Kuznetsov, I.A. Makalkin, M.A. Taylor, A.S. Perelson Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis Bull. Math. Biol 1994 295 321

[17] H. Ledford The perfect blend Nature 2016 162 164

[18] U. Ledzewicz, H. Schättler Application of mathematical models to metronomic chemotherapy: What can be inferred from minimal parameterized models? Cancer Lett. 2017 74 80

[19] U. Ledzewicz, S. Wang, H. Schättler, N. André, M.A.H. Heng, E. Pasquier On drug resistance and metronomic chemotherapy: a mathematical modeling and optimal control approach Math. Biosci. Eng 2017 217 235

[20] K. Leon, K. Garcia, J. Carneiro, A. Lage How regulatory cd25+cd4+t cells impinge on tumor immunobiology? On the existence of two alternative dynamical classes of tumors J. Theor. Biol 2007 122 137

[21] A. Lorz, T. Lorenzi, M.E. Hochberg, J. Clairambault, B. Perthame Populational adaptive evolution, chemotherapeutic resistance and multiple anti-cancer therapies ESAIM: M2AN 2013 377 399

[22] J.D. Martin, G. Seano, R.K. Jain Normalizing function of tumor vessels: Progress, opportunities, and challenges Ann. Rev. Physiol 2019 505 534

[23] F. Meng, J.W. Evans, D. Bhupathi, M. Banica, L. Lan, G. Lorente, J.-X. Duan, X. Cai, A.M. Mowday, C.P. Guise Molecular and cellular pharmacology of the hypoxia-activated prodrug th-302 Mol. Cancer Ther 2012 740 751

[24] S.M. Mumenthaler, J. Foo, N.C. Choi, N. Heise, K. Leder, D.B. Agus, W. Pao, F. Michor, P. Mallick The impact of microenvironmental heterogeneity on the evolution of drug resistance in cancer cells Cancer Inform 2015 19 31

[25] J.D. Murray, Mathematical Biology. Springer-Verlag, Berlin (2002).

[26] E. Piretto, M. Delitala, M. Ferraro Combination therapies and intra-tumoral competition: insights from mathematical modelling J. Theor. Biol 2018 149 159

[27] E. Piretto, M. Delitala, M. Ferraro How combination therapies shape drug resistance in heterogeneous tumoral populations Lett. Biomath 2018 S160 S177

[28] C. Pouchol, J. Clairambault, A. Lorz, E. Trelat Asymptotic analysis and optimal control of an integro-differential system modelling healthy and cancer cells exposed to chemotherapy J. Math. Pures. Appl 2018 268 308

[29] R. Ramakrishnan, D. Assudani, S. Nagaraj, T. Hunter, H.-I. Cho, S. Antonia, S. Altiok, E. Celis, D.I. Gabrilovich Chemotherapy enhances tumor cell susceptibility to ctl-mediated killing during cancer immunotherapy in mice J. Clin. Investig 2010 1111

[30] N.A. Saunders, F. Simpson, E.W. Thompson, M.M. Hill, L. Endo-Munoz, G. Leggatt, R.F. Minchin, A. Guminski Role of intratumoural heterogeneity in cancer drug resistance: molecular and clinical perspectives EMBO Mol. Med 2012 675 684

[31] R. Serre, S. Benzekry, L. Padovani, C. Meille, N. Andre, J. Ciccolini, F. Barlesi, X. Muracciole, D. Barbolosi Mathematical modeling of cancer immunotherapy and its synergy with radiotherapy Cancer Res 2016 4931 4940

[32] Y. Shaked, U. Emmenegger, G. Francia, L. Chen, C.R. Lee, S. Man, A. Paraghamian, Y. Ben-David, R.S. Kerbel Low-dose metronomic combined with intermittent bolus-dose cyclophosphamide is an effective long-term chemotherapy treatment strategy Cancer Res 2005 7045 7051

[33] S. Slovin Chemotherapy and immunotherapy combination in advanced prostate cancer Clin. Adv. Hematol. Oncol 2012 90 100

[34] T. Stiehl, C. Lutz, A. Marciniak-Czochra Emergence of heterogeneity in acute leukemias Biol. Direct 2016 51

[35] D.P. Tabassum, K. Polyak Tumorigenesis: it takes a village Nature Rev. Cancer 2015 473 483

[36] S. Wilson, D. Levy A mathematical model of the enhancement of tumor vaccine efficacy by immunotherapy Bull. Math. Biol 2012 1485 1500

Cité par Sources :